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A body of mass 500 g moves along \mathrm{x}-axis such that it's velocity varies with displacement \mathrm{x} according to the relation v=10 \sqrt{\mathrm{x}} \: \mathrm{m} / \mathrm{s} the force acting on the body is:-

Option: 1

25 \mathrm{~N}


Option: 2

5 \mathrm{~N}


Option: 3

166 \mathrm{~N}


Option: 4

125 \mathrm{~N}


Answers (1)

best_answer

\mathrm{v}=10 \sqrt{\mathrm{x}} \Rightarrow \frac{\mathrm{dv}}{\mathrm{dx}}=\frac{10}{2 \sqrt{\mathrm{x}}}=\frac{5}{\sqrt{\mathrm{x}}}
\mathrm{a}=\mathrm{v} \frac{\mathrm{dv}}{\mathrm{dx}}
\mathrm{a}=\mathrm{v} \times \frac{5}{\sqrt{\mathrm{x}}}=10 \sqrt{\mathrm{x}} \times \frac{5}{\sqrt{\mathrm{x}}}=50 \mathrm{~ms}^{-2}
\mathrm{~F}=\mathrm{ma}=\frac{500}{1000} \times 50=25 \mathrm{~N}

Posted by

Ritika Harsh

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